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Calculus Multivariable
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Table of Contents

Preface. Supplementary Resources. Acknowledgments. About the Authors. C H A P T E R 9 Vectors. Preview. 1 Vectors in the Plane. 2 Vectors in Three-Dimensional Space. 3 The Dot Product and Applications. 4 The Cross Product and Triple Product. 5 Lines and Planes in Space. Summary of Key Topics. Review Exercises. Genesis & Development 9. C H A P T E R 1 0 Vector-Valued Functions. Preview. 1 Vector-Valued Functions?Limits, Derivatives, and Continuity. 2 Velocity and Acceleration. 3 Tangent Vectors and Arc Length. 4 Curvature. 5 Applications of Vector-Valued Functions to Motion. Summary of Key Topics. Review Exercises. Genesis & Development 10. C H A P T E R 1 1 Functions of Several Variables. Preview. 1 Functions of Several Variables. 2 Cylinders and Quadric Surfaces. 3 Limits and Continuity. 4 Partial Derivatives. 5 Differentiability and the Chain Rule. 6 Gradients and Directional Derivatives. 7 Tangent Planes. 8 Maximum-Minimum Problems. 9 Lagrange Multipliers. Summary of Key Topics. Review Exercises. Genesis & Development 11. C H A P T E R 1 2 Multiple Integrals. Preview. 1 Double Integrals Over Rectangular Regions. 2 Integration Over More General Regions. 3 Calculation of Volumes of Solids. 4 Polar Coordinates. 5 Integrating in Polar Coordinates. 6 Triple Integrals. 7 Physical Applications. 8 Other Coordinate Systems. Summary of Key Topics. Review Exercises. Genesis & Development 12. C H A P T E R 1 3 Vector Calculus. Preview. 1 Vector Fields. 2 Line Integrals. 3 Conservative Vector Fields and Path Independence. 4 Divergence, Gradient, and Curl. 5 Green?s Theorem. 6 Surface Integrals. 7 Stokes?s Theorem. 8 The Divergence Theorem. Summary of Key Topics. Review Exercises. Genesis & Development 13. Table of Integrals. Formulas from Calculus: Single Variable. Answers to Selected Exercises. Index.

About the Author

Brian E Blank is an associate professor of mathematics at Washington University in St. Louis. He received his Ph.D. in 1980 at Cornell University, with Anthony Knapp as advisor. His 20th century work involved harmonic analysis. Steven G Krantz is an American scholar, mathematician, and writer. He has authored more than 235 research papers and more than 125 books. Additionally, Krantz has edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.

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